Frequently Asked Questions

Validity of the VM

The vectorial model was initially conceived to take into account that the daugther species are produced with some initial velocity relative to their parent species. This is due to the fact most coma species are produced through a photolytic process that liberates energy. That energy can be converted into kinetic, vibrational or rotational energy. If the coma is not collisional, then the VM formalism breaks down. Since the radius of the coma where collisions are important varies like a few hundred km * Q_parent /1e28, the basic VM model applies to most comet observations. Many phenomena occur in the coma that can limit the validity of the model presented here. Let us mention, and this list is not complete, the variability of the source of parent molecules, the anisotropic ejection of parent molecules, the effect of radiation pressure on the secondary (daughter) and tertiary species (produced from the destruction of the daughter species), the existence of multiple sources for a given species (especially H, O and C). The VM formalism still applies in these latter cases but the code that should be used differs from the one used here.

Steady state assumption

Steady state is a valid assumption when the nucleus output does not vary significantly during the time required to build the coma. The present code calculates the time required to build the coma. This time is directly related to the accuracy of the calculation since limiting it (in theory, it should be infinite) is equivalent to leaving some of the daugther molecules out of the calculations. Given the way the density of coma species varies with distance to the nucleus, a coma of limited extent will affect the calculated column densities depending on the value of the impact parameter of the line of sight that is considered. If this latter is small, even a significant truncation of the line of sight integration will not (or little) affect the results. When the impact parameter of the line of sight becomes of order or greater than the sum of the parent and dautghter species scale lengths, then one should be concerned with the acuracy of the calculations. One empirical way to evaluate the truncation error (e.g. before performing a long series of calculations) is to run the VM for a given set of parameters with a variable coma size (parameters "DESTR" and "DESTP" in the input file). Plotting the column density vs the DESTR parameter allows one to evaluate the error of the code outputs.

What is the difference between the VM presented here and a "Monte Carlo vectorial model"?

The name "Vectorial Model" was coined to indicate that the parent and daughter species velocity vectors combine. Once this basic assumption is accepted, the coma model can be developed in any direction by adding other assumptions. The model presented here assumes simple assumptions like steady activity of the nucleus, an isotropic ejection of the parent molecules, no radiation pressure acting on the parent and daughter species, no production of coma species from grains, ...etc. Once the basic assumptions are selected, there are multiple ways to calculate the VM outputs. The original paper, given its basic assumptions, led to analytical formulae for the density of the coma species. The code employed in this web page calculates the exact density (within the framework selected model assumptions) on a grid of points from which other values are interpolated. Calculation errors are thus reduced to 0.5-1%. When the model contains assumptions that break the general spherical symmetry of the modelled coma, the computation scheme employed here does not work. It is then easier to use a Monte Carlo method to calculate the desired output parameters. In that sense, there is no such thing as a "Monte Carlo" vectorial model. However, some coma models, like those developped by M. Combi (Univ. of Michigan) and that use the Monte Carlo method to derive the model outputs are truly different models. They are in general more elaborated than the basic VM presented here and include more physical phenomena (collisions, optical depth effects, ..etc).

Michel Festou and Joel Parker (joel@boulder.swri.edu)